输入滞后和状态滞后系统的鲁棒H∞控制

针对一类具有状态滞后、输出滞后和凸多面体不确定性的连续时间系统,研究了时滞依赖型鲁棒H_∞控制器的设计问题.通过引入两个附加的松弛矩阵使Lyapunov矩阵和系统矩阵得到分离,得到一个新的鲁棒H_∞性能判据,并基于该判据设计了系统的鲁棒H_∞状态反馈控制器.设计的状态反馈控制器不但保证闭环系统的二次稳定性,同时使系统的H_∞范数小于一个给定的衰减水平.并且设计了一个迭代算法得到问题的次最优解.指出了一种可以在现有的研究成果的基础上得到新的具有更低保守性的性能准则的有效途径.最后通过一个数值算例验证了所提出算法的可行性和优越性.

Robust H∞ control for systems with delayed state and input

The problem of robust H_∞ state feedback controller design for the generalized continuous time systems with time-varying delays in states and control inputs and parameter uncertainties residing in a polytope were investigated. A new improved performance criterion for the existence of robust H_∞ controller was presented by introducing two slack matrices. Then a H_∞ state feedback controller was derived directly from the criterion, which guarantees not only the quadratic stability of the closed-loop systems but also the H_∞ norm bound within a predefined level. The newly proposed criterion exhibits a kind of separation between the systems matrices and the positive definite Lyapunov matrices. As a result, the vertex-dependent Lyapunov functions can be adopted to deliver a less conservative result. An iterative algorithm was developed to further refine the sub-optimal controller. Moreover, this contribution addressed an effective method to obtain new criteria with less conservativeness based on existing research results. A numerical example was employed to illustrate the effect of the proposed approach.